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Electromagnetic fields of a massless charged particle are described by a gauge potential that is almost everywhere pure gauge. Solution of quantum mechanical wave equations in the presence of such fields is therefore immediate and leads to a new derivation of the quantum electrodynamical eikonal approximation. The elctromagnetic action in the eikonal limit is localised on a contour in a two-dimensional Minkowski subspace of four-dimensional space-time. The exact S-matrix of this reduced theory coincides with the eikonal approximation, and represents the generalisatin to electrodynamics of the approach of t Hooft and the Verlindes to Planckian scattering.
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We consider scattering of massless higher-spin particles in the eikonal regime in four dimensions. By demanding the absence of asymptotic superluminality, corresponding to positivity of the eikonal phase, we place constraints on the possible cubic couplings which can appear in the theory. The cubic couplings come in two types: lower-derivative non-abelian vertices, and higher-derivative abelian vertices made out of gauge-invariant curvature tensors. We find that the abelian couplings between massless higher spins lead to an asymptotic time advance for certain choices of polarizations, indicating that these couplings should be absent unless new states come in at the scale suppressing the derivatives in these couplings. A subset of non-abelian cubic couplings are consistent with eikonal positivity, but are ruled out by consistency of the four-particle amplitude away from the eikonal limit. The eikonal constraints are therefore complementary to the four-particle test, ruling out even trivial cubic curvature couplings in any theory with a finite number of massless higher spins and no new physics at the scale suppressing derivatives in these vertices.
We study a class of non-unitary so(2,d) representations (for even values of d), describing mixed-symmetry partially massless fields which constitute natural candidates for defining higher-spin singletons of higher order. It is shown that this class of so(2,d) modules obeys of natural generalisation of a couple of defining properties of unitary higher-spin singletons. In particular, we find out that upon restriction to the subalgebra so(2,d-1), these representations branch onto a sum of modules describing partially massless fields of various depths. Finally, their tensor product is worked out in the particular case of d=4, where the appearance of a variety of mixed-symmetry partially massless fields in this decomposition is observed.
Positive energy unitary irreducible representations of $SU(2,2)$ can be constructed with the aid of bosonic oscillators in (anti)fundamental representation of $SU(2)_Ltimes SU(2)_R$ that are closely related to Penrose twistors. Starting with the correspondence between the doubleton representations, homogeneous functions on projective twistor space and on-shell $SL(2,mathbb C)$ generalized Weyl curvature spinors and their low-spin counterparts, we study in the similar way the correspondence between the massless representations, homogeneous functions on ambitwistor space and, via the Penrose transform, with the gauge fields on Minkowski boundary of $AdS_5$. The possibilities of reconstructing massless fields on $AdS_5$ and some applications are also discussed.
Taking a two interacting scalar toy model with interaction term $gphichi^2$, we study the production of $chi$-particles coming from the decay of an asymptotic and highly occupied beam of $phi$-particles. We perform a non-perturbative analysis coming from parametric resonant instabilities and investigate the possibility that massive $chi$-particles are produced from decays of massless $phi$-particles from the beam. Although this process is not present in a perturbative analysis, our non perturbative approach allows it to happen under certain conditions. For a momentum $p$ of the beam particles and a mass $m_chi$ of the produced ones, we find that the decay is allowed if the energy density of the beam exceeds the instability threshold $p^2mc^4/(2g^2)$. We also provide an analytical expression for the spontaneous decay rate at the earliest time.
We revisit the problem of building consistent interactions for a multiplet of partially massless spin-2 fields in (anti-)de Sitter space. After rederiving and strengthening the existing no-go result on the impossibility of Yang-Mills type non-abelian deformations of the partially massless gauge algebra, we prove the uniqueness of the cubic interaction vertex and field-dependent gauge transformation that generalize the structures known from single-field analyses and in four spacetime dimensions, where our results also hold. Unlike in the case of one partially massless field, however, we show that for two or more particle species the cubic deformations can be made consistent at the complete non-linear level, albeit at the expense of allowing for negative relative signs between kinetic terms, making our new theory akin to conformal gravity. Our construction thus provides the first example of an interacting theory containing only partially massless fields.
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